Becoming a Better Reasoner
Logic Made Easy: How to Know When Language Deceives You.
Deborah J. Bennett. 256 pp. W. W. Norton, 2004. $24.95.
You enter the voting booth and there is a local measure to repeal
term limits. You vote yes. Does this mean you favor term limits?
A mother says to her son, "If you finish your vegetables, you
can have dessert.“ Does this mean that the child must eat all
of his vegetables in order to get dessert?
The answer to the first question is no. If you said otherwise, then
you just voted the wrong way! The answer to the second question: It
all depends. Formal logic (sometimes called classical logic) says
the answer is no. Strictly speaking, the sentence says nothing about
what happens if the child does not finish his vegetables.
Consequently, it is possible for the son to get dessert without
finishing his vegetables. But every parent and child in the world
knows the correct answer is yes: No vegetables, no dessert. Period.
Only grandparents may follow the rules of classical logic in this
situation. Everyone else must follow natural logic, the
logic that underlies the normal, everyday use of language within a society.
These are just two of the many examples Deborah J. Bennett discusses
in her superb little book Logic Made Easy. Some of the
problems she presents will challenge even experts. In particular, a
very clear head is required for the well-known Wason Selection Task
and for the THOG problem, both of which were devised by cognitive
psychologist Peter C. Wason. Many of the other examples Bennett
gives come from the Law School Admission Test (LSAT).
If I were giving a university-level course on logical reasoning,
this would be my textbook, and I would demand that the students read
it from cover to cover. The only caution I would give them would be
to ignore the book's title. In fact, one thing Bennett makes crystal
clear is that logic is anything but easy. Her subtitle, How to
Know When Language Deceives You, is more to the point, and
I suspect that the main title is a product of those in charge of
marketing the book, rather than an attempt by the author to describe
the content. An accurate, but perhaps less salesworthy, title would
be "Logic explained in an entertaining and intelligent
fashion,“ or perhaps "The best introduction to logic
currently available." You get my drift.
By and large, Bennett sticks to the classical propositional logic
that we inherited from the ancient Greeks—and,
or, not, implies, if and only
if—barely mentioning quantification and not covering the
work of Kurt Gödel and Alfred Tarski at all. These are entirely
the right choices, given that this is a book aimed at helping people
from all walks of life to become better reasoners, not a textbook in
logic for mathematics students.
The underlying material is for the most part standard and has been
covered many times by a great many authors. What Bennett brings to
the table are a superb compact history of the subject and a broad
view of the relationship between formal logic and everyday human
reasoning (both features that are sorely lacking in many other books
on logic), backed up by research results from cognitive psychology
and supported by a collection of excellent examples.
In the latter part of the book, Bennett touches on some extensions
of classical Greek propositional logic—such as Venn diagrams,
truth tables, modal logic and fuzzy logic—that bear upon
everyday reasoning. But here, and throughout, for the most part she
stays well clear of mathematical formalisms, and the closest she
gets to mathematical logic is a brief mention of George Boole's
algebra of logic.
In a blurb on the front cover, veteran mathematics writer Martin
Gardner calls the book "The best and the most lucid
introduction to logic you will find." I can't argue with his
logic.—Keith Devlin, Department of Mathematics and
Center for the Study of Language and Information, Stanford